Fractal geometry of texts: An initial application to the works of Shakespeare

@article{Eftekhari2006FractalGO,
  title={Fractal geometry of texts: An initial application to the works of Shakespeare},
  author={Ali Akbar Eftekhari},
  journal={Journal of Quantitative Linguistics},
  year={2006},
  volume={13},
  pages={177 - 193}
}
  • A. Eftekhari
  • Published 1 January 2006
  • Physics
  • Journal of Quantitative Linguistics
Abstract It has been demonstrated that there is a geometrical order in text structures. Fractal geometry, as a modern mathematical approach and a new geometrical standpoint on natural objects including both processes and structures, is here employed for textual analysis. For this first study, the works of William Shakespeare were chosen as the most important items in Western literature. By counting the number of letters in a text, it is possible to study the whole text statistically. A novel… 
Fractal Analysis of Poe's Raven, II*
TLDR
The fractal analysis of Poe's Raven concerns here the original text together with its thirty-three translations and the appropriate segmentation of the poem on each linguistic level is examined from the fractal point of view.
Fractal metaphor LIFE IS A STORY in biographical narrative
Abstract The paper applies an interdisciplinary perspective to a fictional text showing that fractals as mathematical models are a powerful tool for conceptualizing life experience in biographical
Unconscious Patterns in Argument: Fractal Dimension in Oratory
TLDR
Initial results suggest that distinctive “oratorical aims” as may be represented in a text become evident via distinctive fractal dimension.
Generation of a Model for Grapheme Frequencies and its Refinement and Validation by Group Theoretic Aspects
TLDR
A general model for rank frequency distribution of English texts is generated using the patterns of letters in the corpus to derive a functional relationship between ranks and letters of the English language alphabet.
THE EVALUATION OF QUALITY OF A COMPLEX SYSTEM BASED ON THE DISTRIBUTION OF LINKS BETWEEN ITS OBJECTS
TLDR
The empirical criterion of perfection of distribution of the type , where the indices of the degree G and H take on the values ranging from 1 to 4, is suggested for the links ranked in descending order of their intensity -F(N).
Mathematical modeling of the dependence of pattern of occurrence of graphemes in different texts with reference to the occurrence in various words in intra text perspective
  • H. Pande
  • Linguistics, Computer Science
  • 2014
TLDR
The pattern of occurrence of different graphemes of English language has been investigated in intra text perspective and results have been compared for the empirical and theoretical frequencies for the compiled text formed as the composition of all the considered texts.
Mathematical modeling of the frequencies of letters for their occurrence in corpora, words (types) and in the initial positions of words of corpora
Abstract In the present paper an attempt has been made to determine the mathematical model for the frequencies of occurrence of letters in the corpora, in the word types of the corpora and in the
An Analysis of the Multi-scale Structure of Rough Surfaces
.......................................................................................................................................... ii List of Figures
Inquiry into the cultural impact on cost accounting systems (CAS) in Sri Lanka
Purpose - The purpose of this paper is to critically explore the implementation of Cost Accounting Systems (CAS) using Content Analysis (CA). In particular, it aims to examine the impact of Sri
...
...

References

SHOWING 1-10 OF 52 REFERENCES
Are there Fractal Structures in Language? Units of Measurement and Dimensions in Linguistics
TLDR
It is shown that all linguistic quantities introduced so far would be dimensionless, and hence every dependence investigated and every law would be and the consequences for relations between elements on different levels of linguistic a...
A discussion of some aspects of surface fractality and of its determination
There has recently been a rapidly growing interest in using the fractal-geometry approach for the analysis of processes which occur at surfaces with complex morphologies. We discuss a number of
Fractal dimension and classification of music
Zipf's Law and Random Texts
TLDR
It is shown that real texts fill the lexical spectrum much more efficiently and regardless of the word length, suggesting that the meaningfulness of Zipf's law is high.
Zipf's law, the central limit theorem, and the random division of the unit interval.
  • Perline
  • Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
It is shown that a version of Mandelbrot's monkey-at-the-typewriter model of Zipf's inverse power law is directly related to two classical areas in probability theory: the central limit theorem and
Zipf's law is not a consequence of the central limit theorem
It has been observed that the rank statistics of string frequencies of many symbolic systems (e.g., word frequencies of natural languages) follows Zipf's law in good approximation. We show that,
The science of fractal images
TLDR
Fractal Modelling of Real World Images and a Unified Approach to Fractal Curves and Plants are studied.
Self-similarity of the "1/f noise" called music.
  • K. HsüA. Hsü
  • Physics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1991
TLDR
Analyzing Bach's and Mozart's compositions it is shown that the incidence of the frequency intervals, or of the changes of acoustic frequency, has a fractal geometry.
Fractals everywhere
Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal
Fractal geometry - mathematical foundations and applications
TLDR
Applications and examples: fractals defined by transformations examples from number theory graphs of functions examples from pure mathematics dynamical systems iteration of complex functions-Julia sets random fractals Brownian motion and Brownian surfaces multifractal measures physical applications.
...
...